Question

Two workers A and B are engaged to do a piece of work. Working alone, A takes 8 hours more to complete the work than if both worked together. On the,other hand, working alone, 8 would need $4\frac{1}{2}$ hours more to complete the work than if both worked together. How much time would they take to complete the job working together

• A. 4 hours
• B. 5 hours
• C. 6 hours
• D. 7 hours

Answer 1

The correct option is C 6 hours

Let A take x
B take y has together is hours $=(\frac{1}{x}+\frac{1}{y})$ in of work
Let time be t
$t(\frac{1}{x}+\frac{1}{y})+8=\frac{t+8}{x}$
$\frac{t}{y}=\frac{8}{x}$
$t(\frac{1}{x}+\frac{1}{y})=\frac{t+4.5}{y}$
$\frac{t}{x}=\frac{4.5}{y}$
$\frac{x}{y}=\frac{8}{t};\frac{x}{y}=\frac{t}{4.5}$
$\frac{8}{t}=\frac{t}{4.5}$
$\Rightarrow t^2=36$
$t=6hours$.